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  2. scipy stats.foldcauchy () | python

scipy stats.foldcauchy () | python



scipy.stats.foldcauchy () is a folded continuous Cauchy random variable that is defined in a standard format and with some shape parameters to complete its specification.

Parameters:
– & gt; q: lower and upper tail probability
– & gt; a: shape parameters
– & gt; x: quantiles
– & gt; loc: [optional] location parameter. Default = 0
– & gt; scale: [optional] scale parameter. Default = 1
– & gt; size: [tuple of ints, optional] shape or random variates.
– & gt; moments: [optional] composed of letters [`mvsk`]; `m` = mean, `v` = variance, `s` = Fisher`s skew and `k` = Fisher`s kurtosis. (default = `mv`).

Results: folded Cauchy continuous random variable

Code # 1: Create a folded Cauchy continuous random variable Cauchy random variable

from scipy.stats import foldcauchy

  

numargs = foldcauchy.numargs

[a] = [ 0.7 ,] * numargs

rv = foldcauchy (a)

 

< p> print ( "RV:" , rv) 

Exit: 

 RV: & lt; scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D55D8E160 & gt; 

Code # 2: the folded Cauchy random variables and the probability distribution function.

import numpy as np

quantile = np.arange ( 0.01 , 1 , 0.1 )

 
# Random Variants

R = foldcauchy.rvs (a, scale = 2 , size = 10 )

print ( "Random Variates:" , R)

 
# PDF

R = foldcauchy.pdf (a, quantile, loc = 0 , scale = 1 )

print ( "Probability Distribution:" , R) 

Output: 

 Random Variates: [1.7445128 2.82630984 0.81871044 5.19668279 7.81537565 1.67855736 3.35417067 0.13838753 1.29145462 1.90601065] Probability Distribution: [0.42727064 0.42832192 0.43080143 0.43385803 0.43622229 0.43639823 0.4 3294602 0.42480391 0.41154712 0.3934792]

Code # 3: Graphic representation.

import numpy as np

import matplotlib.pyplot as plt

 

distribution = np.linspace ( 0 , np.minimum (rv.dist. b, 3 ))

print ( "Distribution:" , distribution)

 

plot = plt.plot (distributio n, rv.pdf (distribution))

Output: 

 Distribution: [0. 0.06122449 0.12244898 0.18367347 0.24489796 0.30612245 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449 0.67346939 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633 1.10204082 1.16326531 1.2244898 1.28571429 1.34693878 1.40816327 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714 2.20408163 2.26530612 2.32653061 2.3877551 2.44897959 2.51020408 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102 2.93877551 3. ]

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Code # 4: Various Positional Arguments

import matplotlib. pyplot as plt

import numpy as np

 

x = np.linspace ( 0 , 5 , 100 )

 
# Various positional arguments

y1 = foldcauchy.pdf (x, 1 , 3 )

y2 = foldcauchy.pdf (x, 1 , 4 )

plt.plot (x, y1, "*" , x, y2, "r--" )

Output: